{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zX4Kg8DUTKWO"
   },
   "outputs": [],
   "source": [
    "#介绍时间序列\n",
    "\n",
    "\n",
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "w_XJiOdr-MSM"
   },
   "source": [
    "# Lesson 2\n",
    "\n",
    "In the screencast for this lesson I go through a few scenarios for time series. This notebook contains the code for that with a few little extras! :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vidayERjaO5q"
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XpzEXzbHoQhj"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: statsmodels in /home/jupyter-zhaoweidong/.local/lib/python3.7/site-packages (0.12.0)\n",
      "Requirement already satisfied: pandas>=0.21 in /opt/tljh/user/lib/python3.7/site-packages (from statsmodels) (1.0.3)\n",
      "Requirement already satisfied: patsy>=0.5 in /home/jupyter-zhaoweidong/.local/lib/python3.7/site-packages (from statsmodels) (0.5.1)\n",
      "Requirement already satisfied: scipy>=1.1 in /opt/tljh/user/lib/python3.7/site-packages (from statsmodels) (1.4.1)\n",
      "Requirement already satisfied: numpy>=1.15 in /opt/tljh/user/lib/python3.7/site-packages (from statsmodels) (1.18.4)\n",
      "Requirement already satisfied: pytz>=2017.2 in /opt/tljh/user/lib/python3.7/site-packages (from pandas>=0.21->statsmodels) (2020.1)\n",
      "Requirement already satisfied: python-dateutil>=2.6.1 in /opt/tljh/user/lib/python3.7/site-packages (from pandas>=0.21->statsmodels) (2.8.1)\n",
      "Requirement already satisfied: six in /opt/tljh/user/lib/python3.7/site-packages (from patsy>=0.5->statsmodels) (1.12.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install statsmodels --user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gqWabzlJ63nL"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sJwA96JU00pW"
   },
   "outputs": [],
   "source": [
    "def plot_series(time, series, format=\"-\", start=0, end=None, label=None):\n",
    "    plt.plot(time[start:end], series[start:end], format, label=label)\n",
    "    plt.xlabel(\"Time\")\n",
    "    plt.ylabel(\"Value\")\n",
    "    if label:\n",
    "        plt.legend(fontsize=14)\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yVo6CcpRaW7u"
   },
   "source": [
    "# Trend and Seasonality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "t30Ts2KjiOIY"
   },
   "outputs": [],
   "source": [
    "# 1. 生成上升趋势的时间序列\n",
    "def trend(time, slope=0):\n",
    "    return slope * time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iJjc3G1Maefn"
   },
   "source": [
    "Let's create a time series that just trends upward:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BLt-pLiZ0nfB"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = np.arange(4 * 365 + 1)\n",
    "baseline = 10\n",
    "series = trend(time, 0.1)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plot_series(time, series)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WKD4nh9sauBf"
   },
   "source": [
    "Now let's generate a time series with a seasonal pattern:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "89gdEnPY1Niy"
   },
   "outputs": [],
   "source": [
    "# 2. 生成季节性的时间序列\n",
    "def seasonal_pattern(season_time):\n",
    "    \"\"\"Just an arbitrary pattern, you can change it if you wish\"\"\"\n",
    "    return np.where(season_time < 0.4,\n",
    "                    np.cos(season_time * 2 * np.pi),\n",
    "                    1 / np.exp(3 * season_time))\n",
    "\n",
    "def seasonality(time, period, amplitude=1, phase=0):\n",
    "    \"\"\"Repeats the same pattern at each period\"\"\"\n",
    "    season_time = ((time + phase) % period) / period\n",
    "    return amplitude * seasonal_pattern(season_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7kaNezUk1S9l"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "baseline = 10\n",
    "amplitude = 40\n",
    "series = seasonality(time, period=365, amplitude=amplitude)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plot_series(time, series)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-Vo433h0bDLD"
   },
   "source": [
    "Now let's create a time series with both trend and seasonality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AyqFdaIN1oy5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3. 生成既上升又有季节性的时间序列\n",
    "slope = 0.05\n",
    "series = baseline + trend(time, slope) + seasonality(time, period=365, amplitude=amplitude)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plot_series(time, series)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YVdJ2jNN8OHk"
   },
   "source": [
    "# Noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "V4taP424sces"
   },
   "source": [
    "In practice few real-life time series have such a smooth signal. They usually have some noise, and the signal-to-noise ratio can sometimes be very low. Let's generate some white noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3kD3_zjVscBH"
   },
   "outputs": [],
   "source": [
    "# 4. 生成噪声\n",
    "def white_noise(time, noise_level=1, seed=None):\n",
    "    rnd = np.random.RandomState(seed)\n",
    "    return rnd.randn(len(time)) * noise_level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "aLvBwrKrtDzo"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "noise_level = 5\n",
    "noise = white_noise(time, noise_level, seed=42)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plot_series(time, noise)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GHa6gicgbL74"
   },
   "source": [
    "Now let's add this white noise to the time series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2bRDx8K816N9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 5. 将噪声加入到时间序列\n",
    "series += noise\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plot_series(time, series)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a1sQpPjhtj0G"
   },
   "source": [
    "All right, this looks realistic enough for now. Let's try to forecast it. We will split it into two periods: the training period and the validation period (in many cases, you would also want to have a test period). The split will be at time step 1000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_w0eKap5uFNP"
   },
   "outputs": [],
   "source": [
    "split_time = 1000\n",
    "time_train = time[:split_time]\n",
    "x_train = series[:split_time]\n",
    "time_valid = time[split_time:]\n",
    "x_valid = series[split_time:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GICxGswL2aqK"
   },
   "outputs": [],
   "source": [
    "# 6. 自相关\n",
    "def autocorrelation(time, amplitude, seed=None):\n",
    "    rnd = np.random.RandomState(seed)\n",
    "    φ1 = 0.5\n",
    "    φ2 = -0.1\n",
    "    ar = rnd.randn(len(time) + 50)\n",
    "    ar[:50] = 100\n",
    "    for step in range(50, len(time) + 50):\n",
    "        ar[step] += φ1 * ar[step - 50]\n",
    "        ar[step] += φ2 * ar[step - 33]\n",
    "    return ar[50:] * amplitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mCaWIWoDGVCL"
   },
   "outputs": [],
   "source": [
    "def autocorrelation(time, amplitude, seed=None):\n",
    "    rnd = np.random.RandomState(seed)\n",
    "    φ = 0.8\n",
    "    ar = rnd.randn(len(time) + 1)\n",
    "    for step in range(1, len(time) + 1):\n",
    "        ar[step] += φ * ar[step - 1]\n",
    "    return ar[1:] * amplitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "MVM204K66bnC",
    "outputId": "7c6884b9-87ce-43a8-f0d1-7122a944f148"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成不同的时间序列\n",
    "series = autocorrelation(time, 10, seed=42)\n",
    "plot_series(time[:200], series[:200])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "9MZ2sCmM8XPU",
    "outputId": "2f97dc15-0252-46dd-82b5-90837d4d2db6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series = autocorrelation(time, 10, seed=42) + trend(time, 2)\n",
    "plot_series(time[:200], series[:200])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "hqx5et9Bzp5e",
    "outputId": "f705dc4d-5e6a-4b0e-83df-94e112414259"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
    "plot_series(time[:200], series[:200])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "qb5echI7rHqA",
    "outputId": "0695d1b3-2947-4d44-d1c0-2d2cf997e9d5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series = autocorrelation(time, 10, seed=42) + seasonality(time, period=50, amplitude=150) + trend(time, 2)\n",
    "series2 =autocorrelation(time, 5, seed=42) + seasonality(time, period=50, amplitude=2) + trend(time, -1) + 550\n",
    "series[200:] = series2[200:]\n",
    "#series += noise(time, 30)\n",
    "plot_series(time[:300], series[:300])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iBfpCbu6jsaB"
   },
   "outputs": [],
   "source": [
    "#生成脉冲信号图\n",
    "def impulses(time, num_impulses, amplitude=1, seed=None):\n",
    "    rnd = np.random.RandomState(seed)\n",
    "    impulse_indices = rnd.randint(len(time), size=10)\n",
    "    series = np.zeros(len(time))\n",
    "    for index in impulse_indices:\n",
    "        series[index] += rnd.rand() * amplitude\n",
    "    return series    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "BJ1kXWNLg_BD",
    "outputId": "51dba178-72ff-48fc-d280-00ee7c2423fd"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BpnuoVCpUq6elDdZk1py33QIw63PZuWEMNm+kclyFavXU7gWky695i8+nE+3kvHXnJhgbZcmSJVTPOLHrWVJ2Da0DFks6WdIhwAXAqsYGkk4DrgXOjYgdCbOYmRERPPnCtN83+1phdx+NiL3AJcAa4H7gxoi4T9KVks7Nmn0FOAL4nqR7JK2aYXE2AIa3v8C7/scP2TlRvDeiDYZrfrSVf/7FHzL69K7ZG/eR1DsGJB0jiIjVwOqmaVc0XP9gyse3/nLtHQ8z/vxuasNPcv6yQu8gZgW1drje8bDt2ZdY+JZ5OafpHz6y2KygvPtoeRS2a8jMbCZ5n2LCRXR/LgTWc+F34Ruy76BcH5VbGkU+srh0wmfQsh4YhDqa9ykmXET350JgPSe/C83a4jGCApHPoGXWkrzHCIrGXUNmZl02CN1r3eRC0EUeI7BeKvKHWd5jBEXjriEzs5Jz11CBeIygNd591Ky/uBCYmfU5dw0ViMcIrBd8QFn5uGuogNxFZCkNQs9a3ruPuojuz4UgAW8ZmPW3QSim3eRC0EXeErBeKvKHmXcfbY/HCArEWwJmloLHCArIWwZWRu3sFpz3GIHtz4UgAW8ZmFk3uWuoQLwlYL00EHu+DMJz6AF3DRWItwSsF/r1/6zIg9dl50KQgLcMzA7MNaM97hoys/3sG2f1p2nH+nWraibuGiqgov2TmXVDof7rCxU2PRcCs4IZ9C2B2+8fZ/XmJ5I+xuSAr8N2zc07wCDyGIHZLA7wQXzxN9cD8OiXPprw4YtVCTxGYAPDBbI7+vUjrAi/MzH1H1i0LQKPERRQ0b5t9IrXi/WLIhSt6aRK7UJgVlBFPqBs35eCnD6Pi1YH3DVUQO4CsZT69dtsf6aaXtG2Tt01ZGaDK6fvTJOT+TzuG5WqILgQmBXM1GdBn24Y9LVo+lsU7hoys0JopzBFC5/Il35/0xvKc+DHL1YpKHTXkKTlkoYljUi6dJr5h0r6bjb/LkmLUuaxfE2NnRTrLdiHSrICV64b7foyO919tGiFo13JCoGkOcDVwNnAUuBCSUubml0MPBMRvwz8KXBVqjzWRwb7PWXtyG2/imL+E6Ya5E65RXAGMBIRWyPiFWAlcF5Tm/OAb2bXbwI+IBV5pzhrxeSAf7vqFb9TOle0A8pSv9ZKtckj6XxgeUT8Xnb73wLviohLGtrcm7UZy24/nLXZOdNyh4aGYv369W3nuXHdKH+2ZjOHzzu87fu2avz5l3n+5b0cMucgTnrrvI6X8+KuF5Pm7JZ2cz60YwKAY488lKPfdHCqWPsZxHX53Et72PHCbgAWH3tEylivc6CckxE8/OSLwOy5DvQcpv5PWllOuxmnln3cUYdx5GGzn2Fnqv0vH3tE1zde2nnNp3J88eOn8Ml3ndTR40naEBFD080rxLmGJK0AVgBUKhVqtVrbyxgb30vl0Enm6KUup3vN0UfD+pfhN+YL6Pxxjkics1vazbmsMocN469y4ry9wN50wRoM4ro8eh7seKG+PvUG/s86ccCcgmMOFfMOhqNneS4Heg6VeWJ8V3DSUQfNupx2M5527Bzu3vEqC960B9gz67KOO1zs3gvHJPgfauc1X/rWg9jy1CTPjI5Qe+mRrmchIpJcgLOANQ23LwMua2qzBjgruz4X2Em2lTLTZdmyZdGptWvXdnzfXnLO7ilCxgjn7KYiZIzofU5gfczwuZpyjGAdsFjSyZIOAS4AVjW1WQV8Krt+PvCPWWAzM+uRZF1DEbFX0iXUv/XPAa6PiPskXUm9Mq0C/g/wLUkjwNPUi4WZmfVQ0jGCiFgNrG6adkXD9ZeBf50yg5mZHZiPLDYzKzkXAjOzknMhMDMrORcCM7OScyEwMyu5ZKeYSEXSk8AvOrz7fOoHrfU75+yeImQE5+ymImSE3uc8KSLeNt2MwhWCN0LS+pjhXBv9xDm7pwgZwTm7qQgZob9yumvIzKzkXAjMzEqubIXgurwDtMg5u6cIGcE5u6kIGaGPcpZqjMDMzF6vbFsEZmbWpDSFQNJyScOSRiRdmmOOhZLWStoi6T5Jn82mv0XSDyQ9lP19czZdkv48y71J0uk9zjtH0t2Sbs5unyzprizPd7NTjCPp0Oz2SDZ/UQ8zHiPpJkkPSLpf0ln9tj4l/efs9b5X0g2SDuuHdSnpekk7sl8LnJrW9rqT9Kms/UOSPjXdYyXI+ZXsNd8k6f9KOqZh3mVZzmFJH2mYnvRzYLqcDfM+Lykkzc9u57Y+X2emHyoYpAv102A/DLwdOATYCCzNKcvxwOnZ9SOBB4GlwJeBS7PplwJXZdfPAW6l/jPfZwJ39Tjv54DvADdnt28ELsiuXwP8++z6fwCuya5fAHy3hxm/Cfxedv0Q4Jh+Wp/ACcAjwJsa1uFF/bAugfcCpwP3Nkxra90BbwG2Zn/fnF1/cw9yfhiYm12/qiHn0uw9fihwcvben9OLz4HpcmbTF1I/Jf8vgPl5r8/X5U79JuiHCy38WlqO2f4e+BAwDByfTTseGM6uXwtc2NB+X7seZFsA3A68H7g5+4fd2fDm27de6eDX5rqU8ejsQ1ZN0/tmfVIvBKPZG3tuti4/0i/rEljU9AHb1roDLgSubZi+X7tUOZvmfRz4dnZ9v/f31Prs1efAdDmBm4B3Ao/yWiHIdX02XsrSNTT1Rpwylk3LVbbJfxpwF1CJiCeyWduBSnY9z+x/BvwXYDK7/Vbg2YiY+sHhxiz7cmbzn8vap3Yy8CTwl1kX1l9IOpw+Wp8RsQ34KvAY8AT1dbOB/luXU9pdd/3w/vpd6t+uOUCeXHJKOg/YFhEbm2b1Tc6yFIK+I+kI4PvAf4qI5xvnRf1rQK67c0n6GLAjIjbkmaMFc6lviv+viDgNeJF6d8Y+ea/PrI/9POpF65eAw4HleeVpR97rrhWSLgf2At/OO0szSfOAPwKumK1tnspSCLZR76ObsiCblgtJB1MvAt+OiL/NJo9LOj6bfzywI5ueV/b3AOdKehRYSb176OvAMZKmftmuMcu+nNn8o4GnepBzDBiLiLuy2zdRLwz9tD4/CDwSEU9GxB7gb6mv335bl1PaXXe5vb8kXQR8DPhkVrQ4QJ48cr6D+heAjdl7aQHwc0nH9VPOshSCdcDibC+NQ6gPwK3KI4gkUf+t5vsj4msNs1YBU3sHfIr62MHU9N/J9jA4E3iuYbM9mYi4LCIWRMQi6uvrHyPik8Ba4PwZck7lPz9rn/ybZERsB0YlLckmfQDYQn+tz8eAMyXNy17/qYx9tS4btLvu1gAflvTmbOvnw9m0pCQtp951eW5E7GrKf0G299XJwGLgZ+TwORARmyPi2IhYlL2XxqjvLLKdflqfKQcg+ulCfYT+Qep7DVyeY45/QX1TexNwT3Y5h3of8O3AQ8APgbdk7QVcneXeDAzlkLnKa3sNvZ36m2oE+B5waDb9sOz2SDb/7T3MdyqwPlunf0d9T4u+Wp/AfwMeAO4FvkV9j5bc1yVwA/Vxiz3UP6Qu7mTdUe+jH8kun+5RzhHqfelT76NrGtpfnuUcBs5umJ70c2C6nE3zH+W1weLc1mfzxUcWm5mVXFm6hszMbAYuBGZmJedCYGZWci4EZmYl50JgZlZyLgRmM5D0Vkn3ZJftkrZl1yckfSPvfGbd4t1HzVog6QvARER8Ne8sZt3mLQKzNkmq6rXfZ/iCpG9K+n+SfiHpE5K+LGmzpNuy04kgaZmkH0naIGnN1CkczPqBC4HZG/cO6udiOhf4G2BtRPw68BLw0awY/E/g/IhYBlwPfDGvsGbN5s7exMxmcWtE7JG0mfqPn9yWTd9M/dz0S4BTgB/UTzXEHOqnITDrCy4EZm/cboCImJS0J14beJuk/h4TcF9EnJVXQLMDcdeQWXrDwNsknQX105BL+mc5ZzLbx4XALLGIeIX66aSvkrSR+pky351vKrPXePdRM7OS8xaBmVnJuRCYmZWcC4GZWcm5EJiZlZwLgZlZybkQmJmVnAuBmVnJuRCYmZXc/wexFgMYL+8NbAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series = impulses(time, 10, seed=42)\n",
    "plot_series(time, series)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "uvMAqSatkcyX"
   },
   "outputs": [],
   "source": [
    "def autocorrelation(source, φs):\n",
    "    ar = source.copy()\n",
    "    max_lag = len(φs)\n",
    "    for step, value in enumerate(source):\n",
    "        for lag, φ in φs.items():\n",
    "            if step - lag > 0:\n",
    "              ar[step] += φ * ar[step - lag]\n",
    "    return ar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "iUv8l8nchJRZ",
    "outputId": "97676db8-78cc-4f13-dd5c-3e38b569164e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "signal = impulses(time, 10, seed=42)\n",
    "series = autocorrelation(signal, {1: 0.99})\n",
    "plot_series(time, series)\n",
    "plt.plot(time, signal, \"k-\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "5_lx-AlWhT5v",
    "outputId": "9d359a3d-a00b-432d-b4be-d565d976febb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "signal = impulses(time, 10, seed=42)\n",
    "series = autocorrelation(signal, {1: 0.70, 50: 0.2})\n",
    "plot_series(time, series)\n",
    "plt.plot(time, signal, \"k-\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "id": "nWQ9fvFAOGRB",
    "outputId": "eddd8f75-dc13-425c-d89c-2f7b93d3bb17"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series_diff1 = series[1:] - series[:-1]\n",
    "plot_series(time[1:], series_diff1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "id": "AvUI22RSONQd",
    "outputId": "23dce7f5-2561-45d8-af44-2e33b7898d2b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f114d6e32e8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas.plotting import autocorrelation_plot\n",
    "\n",
    "autocorrelation_plot(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 493
    },
    "colab_type": "code",
    "id": "ddRJGI1pic78",
    "outputId": "3eed467f-64e9-4ccb-b3e0-756c94f6c3a8"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyter-zhaoweidong/.local/lib/python3.7/site-packages/statsmodels/tsa/arima_model.py:472: FutureWarning: \n",
      "statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have\n",
      "been deprecated in favor of statsmodels.tsa.arima.model.ARIMA (note the .\n",
      "between arima and model) and\n",
      "statsmodels.tsa.SARIMAX. These will be removed after the 0.12 release.\n",
      "\n",
      "statsmodels.tsa.arima.model.ARIMA makes use of the statespace framework and\n",
      "is both well tested and maintained.\n",
      "\n",
      "To silence this warning and continue using ARMA and ARIMA until they are\n",
      "removed, use:\n",
      "\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARMA',\n",
      "                        FutureWarning)\n",
      "warnings.filterwarnings('ignore', 'statsmodels.tsa.arima_model.ARIMA',\n",
      "                        FutureWarning)\n",
      "\n",
      "  warnings.warn(ARIMA_DEPRECATION_WARN, FutureWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             ARIMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                    D.y   No. Observations:                 1460\n",
      "Model:                 ARIMA(5, 1, 0)   Log Likelihood                2223.428\n",
      "Method:                       css-mle   S.D. of innovations              0.053\n",
      "Date:                Sat, 31 Oct 2020   AIC                          -4432.855\n",
      "Time:                        14:09:49   BIC                          -4395.852\n",
      "Sample:                             1   HQIC                         -4419.052\n",
      "                                                                              \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0003      0.001      0.384      0.701      -0.001       0.002\n",
      "ar.L1.D.y     -0.1235      0.026     -4.714      0.000      -0.175      -0.072\n",
      "ar.L2.D.y     -0.1254      0.029     -4.333      0.000      -0.182      -0.069\n",
      "ar.L3.D.y     -0.1089      0.029     -3.759      0.000      -0.166      -0.052\n",
      "ar.L4.D.y     -0.0914      0.029     -3.162      0.002      -0.148      -0.035\n",
      "ar.L5.D.y     -0.0774      0.029     -2.675      0.007      -0.134      -0.021\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1            1.0145           -1.1311j            1.5194           -0.1336\n",
      "AR.2            1.0145           +1.1311j            1.5194            0.1336\n",
      "AR.3           -1.8173           -0.0000j            1.8173           -0.5000\n",
      "AR.4           -0.6967           -1.6113j            1.7554           -0.3150\n",
      "AR.5           -0.6967           +1.6113j            1.7554            0.3150\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "#!pip install statsmodels\n",
    "#!pip install statsmodels --target=/opt/tljh/user/lib/python3.7/site-packages\n",
    "\n",
    "#from statsmodels import tsa\n",
    "#from statsmodels.tsa.arima_model import ARIMA\n",
    "#path = '/home/jupyter-zhaoweidong/.local/lib/python3.7/site-packages/'\n",
    "#model = ARIMA(series, order=(5, 1, 0))\n",
    "#model_fit = model.fit(disp=0)\n",
    "#print(model_fit.summary()) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "A0l79ROF1xu1"
   },
   "outputs": [],
   "source": [
    "#import pandas as pd\n",
    "#df = pd.read_csv(\"sunspots.csv\", parse_dates=[\"Date\"], index_col=\"Date\")\n",
    "#series = df[\"Monthly Mean Total Sunspot Number\"].asfreq(\"1M\")\n",
    "#series.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wVoq4cmx3-vk"
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'plot'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-46-be382de3b8c2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mseries\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'plot'"
     ]
    }
   ],
   "source": [
    "#series.plot(figsize=(12, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "stmDLe8jEDQL"
   },
   "outputs": [],
   "source": [
    "#series[\"1995-01-01\":].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "SXc9PkCXJd_a"
   },
   "outputs": [],
   "source": [
    "#series.diff(1).plot()\n",
    "#plt.axis([0, 100, -50, 50])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "G1T-V7B8180O"
   },
   "outputs": [],
   "source": [
    "#from pandas.plotting import autocorrelation_plot\n",
    "\n",
    "#autocorrelation_plot(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8jdIxEASH_1z"
   },
   "outputs": [],
   "source": [
    "#autocorrelation_plot(series.diff(1)[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6eIY8wloG3Go"
   },
   "outputs": [],
   "source": [
    "#autocorrelation_plot(series.diff(1)[1:].diff(11 * 12)[11*12+1:])\n",
    "#plt.axis([0, 500, -0.1, 0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "El2JSNZwG7UP"
   },
   "outputs": [],
   "source": [
    "#autocorrelation_plot(series.diff(1)[1:])\n",
    "#plt.axis([0, 50, -0.1, 0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gvmZAKeAHACf"
   },
   "outputs": [],
   "source": [
    "#116.7 - 104.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ReEbS1MpC50n"
   },
   "outputs": [],
   "source": [
    "#[series.autocorr(lag) for lag in range(1, 50)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7rdXm2UX3WsH"
   },
   "outputs": [],
   "source": [
    "#pd.read_csv(filepath_or_buffer, sep=',', delimiter=None, header='infer', names=None, index_col=None, usecols=None, squeeze=False, prefix=None, mangle_dupe_cols=True, dtype=None, engine=None, converters=None, true_values=None, false_values=None, skipinitialspace=False, skiprows=None, skipfooter=0, nrows=None, na_values=None, keep_default_na=True, na_filter=True, verbose=False, skip_blank_lines=True, parse_dates=False, infer_datetime_format=False, keep_date_col=False, date_parser=None, dayfirst=False, iterator=False, chunksize=None, compression='infer', thousands=None, decimal=b'.', lineterminator=None, quotechar='\"', quoting=0, doublequote=True, escapechar=None, comment=None, encoding=None, dialect=None, tupleize_cols=None, error_bad_lines=True, warn_bad_lines=True, delim_whitespace=False, low_memory=True, memory_map=False, float_precision=None)\n",
    "#Read a comma-separated values (csv) file into DataFrame.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sYXNHu_trIH2"
   },
   "outputs": [],
   "source": [
    "#from pandas.plotting import autocorrelation_plot\n",
    "\n",
    "#series_diff = series\n",
    "#for lag in range(50):\n",
    "#  series_diff = series_diff[1:] - series_diff[:-1]\n",
    "\n",
    "#autocorrelation_plot(series_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "s6SVHBpqrO1X"
   },
   "outputs": [],
   "source": [
    "#import pandas as pd\n",
    "\n",
    "#series_diff1 = pd.Series(series[1:] - series[:-1])\n",
    "#autocorrs = [series_diff1.autocorr(lag) for lag in range(1, 60)]\n",
    "#plt.plot(autocorrs)\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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